Nasheed, who took refuge in the Indian High Commission here Wednesday after a court ordered his arrest, said Hassan cannot be trusted to hold a free and fair presidential election.
"The events of the past year - the mass arrests, police brutality, the politically motivated trials - demonstrate that Waheed cannot be trusted to hold a free and fair election," said Nasheed in a statement posted on the website of his Maldivian Democratic Party.
"Waheed should do the right thing and resign from office," he said.
"An interim, caretaker government should be established that can lead the Maldives to genuinely free and fair elections, in which all candidates are freely able to compete."
Nasheed, 45, entered the Indian mission after a court issued an arrest order after he failed to attend a scheduled hearing over the detention of Criminal Court chief judge Abdulla Mohamed.
Nasheed resigned Feb 7 last year followed by what he alleged was a coup. Vice President Mohammed Waheed Hassan succeeded him.
The statement on mdp.org.mv quoted him as describing his ongoing trial against him as "a politically motivated sham".
He said the Hulhumale Magistrates Court - established to hear his case - was illegal and created "with the sole purpose of disqualifying me from the presidential elections".
He accused Waheed of ruling the Maldives with "the barrel of a gun".
The Maldives, an atoll nation, is known for its deep blue seas, turquoise reefs, white sandy beaches and palm trees. It comprises 1,190 islands - of which about 200 are inhabited - and has a population of 350,000.
The country has been in political turmoil even since Nasheed was ousted.
Male: Maldivian President Mohammed Waheed Hassan must quit and an interim, caretaker government should be set up, former president Mohamed Nasheed demanded Thursday.
First Published: Thursday, February 14, 2013, 14:02